{
  "id": "2105.10921",
  "version": "v1",
  "published": "2021-05-23T11:59:55.000Z",
  "updated": "2021-05-23T11:59:55.000Z",
  "title": "Tabulation of knots up to five triple-crossings and moves between oriented diagrams",
  "authors": [
    "Michał Jabłonowski"
  ],
  "comment": "15 pages, many TikZ figures",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We enumerate and show tables of minimal diagrams for all prime knots up to the triple-crossing number equal to five. We derive a minimal generating set of oriented moves connecting triple-crossing diagrams of the same oriented knot. We also present a conjecture about a strict lower bound of the triple-crossing number of a knot related to the breadth of its Alexander polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-23T11:59:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "oriented diagrams",
      "tabulation",
      "strict lower bound",
      "triple-crossing number equal",
      "minimal generating set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}